First, halve the second coefficient (-2) and then square it:
-2/2 = -1, (-1)^2 = 1, then add it to both sides:
[tex] x^{2} -2x +1 = 1[/tex]
Now on the left side, we can rewrite this as:
[tex] x^{2} - x - x + 1 = 1[/tex]
Factor out an x from the first two terms:
[tex]x(x-1) - x + 1 = 1[/tex]
Factor out a -1 from the last two terms:
[tex]x(x-1) - 1(x-1) = 1[/tex]
Now we can rewrite it as:
[tex](x-1)(x-1) = 1[/tex]
Which is equal to:
[tex](x-1)^{2} = 1[/tex]
Square root both sides, keeping in mind that leaves us with plus or minus one on the right:
[tex](x-1) = 1[/tex]
[tex](x-1) = -1[/tex]
Add one to both sides in both equations to solve for our two roots:
[tex]x = 2, 0[/tex]
